Dispersion of proton spin-lattice relaxation time in laboratory and rotating frame of healthy and tumorous mice tissues will be studied at different temperatures. The dispersion data at room temperature indicate that: (a) Rotational motion of bound water molecules will slow down if the tissue is cooled. This mechanism will become less effective in relaxing the majority ("free") water protons. (b) The diffusion of free water will slow down if the tissues is cooled. This mechanism will become more effective in relaxing the water protons. (c) The thermal contact between bound and free water is provided by proton exchange. This mechanism relaxes the Zeeman energy reservoir in the rotating frame but does not contribute directly to the Zeeman energy relaxation at high field. As the temperature is lowered the exchange slows down and the thermal contact between the two types of water is getting weaker. Also, the relaxation rate (Tl rho-1) due to this mechanism will decrease with decreasing temperature. By varying the temperature and the rotating frame field strength we plan to find the condition under which the effect of cancer (increased water content in tumor itself and in many healthy tissues) can be observed (in vitro) with greatest resolution (Proton Spin Relaxation in tissues, R.R. Knispel, R.T. Thompson and M.M. Pintar, to be published in J. Mag. Ressonance, preprint available).